Is it standard now to 4! shove say TT+/AQs+ in some situations, but flat call 99/AJs and shove some weaker hands that play decently versus a calling range? I suppose that would also apply to 3! and 5! shoves. Is the idea to weaken your shoving range and play strong hands not in a value shoving range postflop? Was this developed by people or solvers? It seemed strange to me, because if you are going allin preflop, if can be a semibluff but not really a bluff. I don't play by formula and such, but I am just interested in the theory.

Really hard to answer any of this without context. Modern MTT ranges are calculated with solvers and ICM software.

if they're not 3 betting 88 nor ATs, then 4 bet shoving 99 and AJs makes no sense. implied is that there are many big blinds in play since the 3 bet is not all in as posed in op. as such, the value of calling the 3 bet must be considered. think about how 88 and ATs perform vs the opponent's opening range(probably quite profitable vs most ranges even early position 2x, 2.5x, 3x raises). now why would you want to forgo that ev in favor of 3 betting for less profit?

thus if ev call > ev 3 bet ----> call

if ev 3 bet > ev call ----> 3 bet

if ev call 3 bet > ev shove -----> call

if ev shove > ev call 3 bet ----> shove

im making the assumption that we're not close to the bubble because bubble play usually features much shorter stacks that dictate (3 bet = shove) in most spots; 4 betting is rarely an option near the bubble. however if 4 betting is an option near the bubble then you must consider how often you wlll be eliminated from the tourney if you 4 bet shove. if your opponent is the type to call a lot, then perhaps just calling the 3 bet is superior in terms of (tourney prize pool ev) while vs players that tend to fold a lot 4 betting mroe often is recommended. vs experts that will call the shove at near optimal frequencies with the right hands, lots of metagame stuff comes into play:

a) my image (have i been raising preflop a lot, or have i been folding a lot)

b) the opponents willingness to change strategy to exploit my image.

c) the other players left in the hand that could wake up with big hands.

d) the tendencies of the other players.

e) the steepness of the payout curve (top heavy payouts favor the bold, while flat curves favor the reserved).

regarding the question of preflop "bluffs":

think about the addition of marginal hands to the 4 bet shoving range. if you had to pick either 99 or A5s, ask yourself which one benefits the range more. 99 will typically cause the opponent to fold more, costing the range as a whole(because big hands don't win as many chips on average), while A5s would cause the opponent to call more, benefiting the range as a whole(as now big hands win more chips).